Chapter 21, Problem 21P

An 11-m beam is subjected to a load, and the shear force follows the equation

$V\left(x\right)=5+0.25x^2$

whereV is the shear force and x is length in distance along the beam. We know that $V=dM/dx,$ and M is the bending moment. Integration yields the relationship

$M=M_0+{\displaystyle {\int }_0^{x}Vdx}$

If $M_0$ is zero and $x=11$ calculate M using

(a) Analytical integration,

(b) Multiple-application trapezoidal rule, and

(c) Multiple-application

Simpson's rules. For (b) and (c) use 1-m increments.